Hi lincs-b
I've just been doing a bit of net-trawling relating to med physics careers, for my own nefarious reasons as a practising UK med physicist. Although I'm new to this forum your post caught my eye & thought i'd give you a UK based answer as the route, practice, terminology & respective recognition differs depending on which country you are in.
Firstly, never mind a specialty, are you sure you've decided on med physics so early on in your degree course? Have you tried approaching med physics depts in hospitals for work experience or a short visit? Consider it in the same way that a prospective medical student must approach a Med School - if you have evidence of initiative, searching out and getting experience in the field, even if just a few days or weeks, then that sorts out the vaguely interested from the dedicated applicants.
Are you doing med physics degree or options relating to it? If not, don't worry - most don't. The idea of the first degree is to give you specific skills and knowledge relating to physics, such as the grounding in anat/physiol/pharm does for medics, and it's the role of the accredited Masters degree & subsequent on the job training to provide the specialist knowledge and skills you would need to be a professional MP.
You need to look at the website for the UK Medical Physics professional body - the IPEM - as they hold information on the training scheme (which is roughly the equivalent of the residency programme in US & Cananda). The training scheme has a competitive entry and limited places, so good grades, supporting evidence such as experience and non-academic activities that provide personal development eg communication skills will help you compete.
Roughly 50-100 applicants per post, but view that as a challenge, not a brick wall, and then you've got the right frame of mind to approach it with.
The training is fully funded, you are in a paid post, it's a career not a student haven, so expect full time hours with some late working when required (access to scanners/linacs etc doesn't always happen in office hours) and studying in your own time to augment & consolidate what you are doing in your training post. The best thing is that you won't be on-call and won't usually need to work weekends. That's the trade-off for not getting paid nearly as much as the medics...
If you don't possesses an accredited Masters degree in Medical Physics when you apply you will do this as part of your Part 1 training in the first 2 years. This MSc is a pre-requisite for continuing in the profession for those who enter without a relevant PhD, even with a PhD you may need to augment your knowledge areas in clinical and physical science areas which you lack.
The Part 1 training will cover 3 main specialist areas of medical physics and you don't normally need to know which you wish to specialise in for Part 2 training until near the end of year 2. Usually. Areas of specialisation include radiotherapy, nuclear medicine/PET, diagnostic radiology, radiation protection, MR, physiological measurement, engineering / rehab, non-radiation (lasers/ultrasound)...some may be combined.
In the UK we are called Medical Physicists (as a type of Clinical Scientist - a title which is protected on the Professional Register) or Clinical Physicists - these terms are used by physicists working in hospitals, whether they work in diagnostic radiology, radiation protection, nuclear medicine, radiotherapy etc. If someone is a Health Physicist this is normally used by those working outside of the hospital setting, such as in industrial setting (eg nuclear power stations) or for public or private consultancy firms providing radiation protection services.
By contrast in the US it seems that Health Physicist is used to denote someone who works in the radiation protection area (which encompasses diagnostic radiology support) but Medical / Clinical denotes someone working in radiotherapy applications in hospitals.
Be aware of the differences when you read a lot of posts from a US perspective and be aware that differences exist depending on which job you choose within the UK.
My own area of Nuclear Medicine is very clinically orientated and physicists working here have a lot of patient contact, we even provide some diagnostic and radionuclide therapy services within the hospital. My work cuts across the boundaries of Health and Medical Physicist as defined in the US way, I have to give RP advice one minute, do a dose calculation for a patient treatment the next, deal with computers, scanners, radiopharmacy, QA, teaching, training, joint-reporting, MDT meetings ...I have so many different hats to wear but it's always challenging in some way. The best recommendation I have is that it's so hard for Med Physicists to tell you what they actually do, because no two days are alike.
Part-time PhD study is possible in some jobs, usually encouraged, but you have to find subject and funding that is appropriate - but there are PhD's worldwide to choose from if you want to do this full time before applying for the training scheme. It may take less time in fact than doing it alongside a job as you can concentrate on it - colleagues taking 7 years or more to do their PhD seems a little long to me.
Anyway, have a look at the training scheme info provided by IPEM and HPC and don't forget to enjoy your time at Uni too.
All the best.